A uniform disc of mass 20 kg and radius 0.5 m can turn about a smooth axis through its centre and perpendicular to the disc. A constant torque is applied to the disc for 3s from rest and the angular velocity at the ned of that time is `(240)/(pi)rev//min` find the magnitude of the torque. if the torque is then removed and the disc is brought to rest in `t` seconds by a constant force of 10 N applied tangentially at a point on the rim of the disc, find `t`

Explanation

To solve the problem step by step, we will first find the torque applied to the disc and then calculate the time `t` it takes to bring the disc to rest after the torque is removed.

### Step 1: Convert Angular Velocity to Radians per Second
The angular velocity given is \( \frac{240}{\pi} \) revolutions per minute (rev/min). We need to convert this to radians per second (rad/s).

\[ \omega = \frac{240}{\pi} \text{ rev/min} \times \frac{2\pi \text{ rad}}{1 \text{ rev}} \times \frac{1 \text{ min}}{60 \text{ s}} = \frac{240 \times 2\pi}{60\pi} = 8 \text{ rad/s} \]
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